Abstract: A displacement-type ring gear machine includes a casing including a gear chamber comprising a supply port and a discharge port, an internal gear accommodated in the gear chamber and comprising an external toothing, and an external gear eccentric to the internal gear and comprising an internal toothing meshing with the external toothing so as to form expanding and contracting fluid cells which direct the working fluid from the supply port to the discharge port. The meshing toothings comprise a radial clearance and a tangential clearance which is smaller than the radial clearance. The tips or roots of at least one of the two toothings comprise a profile derived from a cycloid.